I'd certainly recommend it for the transport. (There are, I believe, other reasons to visit.)
As well as trains of various types, the metro lines, the tram line and funiculars you also have street escalators, travelators, lifts and a transporter bridge.
And none of the track is (currently) standard gauge. Not many places with lots of track in two gauges and neither of them is standard.
The bus and coach system in the area is also impressive and it has the nicest underground coach station I've ever seen.
I concur. Bilbao is a great city to visit (in no particular order: football, Guggenheim, food, transport, Plaza Nueva on a Saturday night, architecture, Poza on a match day, old town...)
I would recommend getting a Barik card for travelling around, covers transport all over Bizkaia and makes travelling very cheap. Valid on bus, tram, metro, Eusketren, Feve, Renfe, transporter bridge, funicular...
Pays for itself on the first return trip on the airport bus (5 euro for the card then 70 cents for the journey, I think the full fare is 4.50 single). Unfortunately there isn't a machine to buy one at the airport so you have to wait until you get into the city. Load it up on a machine or via a phone app then tap in/tap out.